{"as_of":"2026-08-14T12:55:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d997b646c11a3eeaba2adcdcf7503848d68018b03d3927aae1256d90fc93754c","coverage":[{"denominator":26,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":26,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T00:15:55.087825Z","state":"measured"},{"denominator":26,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":26,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2608.08322/citation-record","integrity":"/paper/2608.08322/integrity","json":"/paper/2608.08322/citation-record.json","paper":"/paper/2608.08322"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:54.681560Z","title":"Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations.Journal of Computational Physics, 79(1):12–49, 1988","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:54.681560Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:9e8d88a37ae20ce9317d0a13ec50d60b58ddd3c85dab57dbb76501fc634b68b4","observation_id":"13b0aa15-afdf-4384-b156-5b44f9423c71","resolution":{"observed_at":"2026-08-12T00:15:54.681560Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:54.686164Z","title":"A Level Set Approach for Com- puting Solutions to Incompressible Two-Phase Flow.Journal of Computational Physics, 114(1):146–159, 1994","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:54.686164Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:38a5ec86729198cfd5297f0c74998593625a33f030cb5ab69f29fd5dacd7aa27","observation_id":"172b0b0d-5925-4d1d-90de-35dc0b36ad4c","resolution":{"observed_at":"2026-08-12T00:15:54.686164Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:57.013052Z","title":"An Efficient, Interface-Preserving Level Set Re- distancing Algorithm and Its Application to Interfacial Incompressible Fluid Flow","venue":null,"work_id":"17975639-a921-4e7c-b1fa-6a175c761fae","year":1999},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:54.693816Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:8ad9c5efb34b0d2972f047efe48703b690502203169e98fae3e472d17a06f861","observation_id":"31666ef3-036c-46fc-9702-b6fccf81c16e","resolution":{"observed_at":"2026-08-12T00:15:57.017090Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:54.705562Z","title":"Raissi, P","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:54.705562Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:56ce658f0612555779e9ac5024b8855f2aa5e1b57448536c62d6c35d8242dab4","observation_id":"d0dfb301-f372-4d6c-b23e-d74c65439709","resolution":{"observed_at":"2026-08-12T00:15:54.705562Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:56.998090Z","title":"Krishnapriyan, Amir Gholami, Shandian Zhe, Robert M","venue":null,"work_id":"3be8e34b-e699-4365-a139-35d1e5fcdd66","year":2021},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:54.754748Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:9d3d5226d7e5ee80e53394981a2fa8b9af17bc7572885d85874b7eb4be8cc682","observation_id":"545df80b-71a2-4e9a-aa5f-ba2e4ac43280","resolution":{"observed_at":"2026-08-12T00:15:57.002999Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1063/5.0289386","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:55.395994Z","title":"Physics- informed neural networks for solving moving interface flow problems using the level set approach.Physics of Fluids, 37(10):107124, 2025","venue":null,"work_id":"f99f2189-ad49-49d2-9f70-732caa21f495","year":2025},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:54.767635Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:5f2460cd7282b40e15a1f443fda48a7b3679191f33a572eea44e880203d2a54f","observation_id":"89f5e251-3f5f-454d-bcec-38c109a4479c","resolution":{"observed_at":"2026-08-12T00:15:55.419076Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-12T23:38:13.244122+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-12T23:38:13.244122+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:56.979123Z","title":"Extended Interface Physics-Informed Neural Networks Method for Moving Interface Problems, 2026","venue":null,"work_id":"802b8059-f51d-4256-85fe-54fd7aac03ad","year":2026},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:54.774894Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:fbaa23c63c170d3f4241bdb3cfcfa24287d95b271d532992a76e369c28047e7d","observation_id":"52e86073-64f2-49a2-bdf3-42b78def65ac","resolution":{"observed_at":"2026-08-12T00:15:56.987836Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:56.942842Z","title":"Physics-informed neural networks for solving two-phase flow problems with moving interfaces, 2026","venue":null,"work_id":"220fdf1e-004e-438d-9e16-a3227d7ecb41","year":2026},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:54.795029Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:98ab70399b2557393136dd6fe9e226712a1f174b98051c247294ea89cbcb7176","observation_id":"27944279-d60a-4a6f-a681-f452b50557ad","resolution":{"observed_at":"2026-08-12T00:15:56.959108Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:56.855563Z","title":"Physics-Informed Machine Learning for Two-Phase Moving-Interface and Stefan Problems, 2025","venue":null,"work_id":"cb0c79fe-9de2-4615-b5a0-66f33cd80892","year":2025},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:54.804251Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:3335de818acd00a2ab8d967f5c63d1c9df8ff0c1a3f8ebd492eb9d4ffc08d2d4","observation_id":"b0da4afd-c310-4d5c-b88e-b7d2b244eb89","resolution":{"observed_at":"2026-08-12T00:15:56.916444Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:54.808063Z","title":"A systematic study of physics-informed neural networks for the level-set interface advection.Machine Learning: Science and Technology, 7(4):045032, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:54.808063Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:9fe7050b0fe3ad6915fb44d16ac6e3ad8b8281858bcb294735595312e2f74a51","observation_id":"315f2f93-ec56-4f80-a23d-4048eb9f072f","resolution":{"observed_at":"2026-08-12T00:15:54.808063Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:54.811532Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:54.811532Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:16419d88a2cc0afaba339273ae06120902e68a67d9181793f7ee8172387d68c2","observation_id":"1cda0c30-f918-41ce-8330-96a4c19b478d","resolution":{"observed_at":"2026-08-12T00:15:54.811532Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:56.764382Z","title":"DeepXDE: A Deep Learning Library for Solving Differential Equations.SIAM Review, 63(1):208–228,","venue":null,"work_id":"0d768a07-2fd4-47b7-aec1-05ccff9656d4","year":null},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:54.836672Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:f672e39c97463d669c6ce15c076a828599770c5357e780e23f2a5e74909200ed","observation_id":"cd84415e-5498-4b57-8bf8-0366e4bfbcbe","resolution":{"observed_at":"2026-08-12T00:15:56.807364Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:54.882598Z","title":"Understanding and Mitigating Gra- dient Flow Pathologies in Physics-Informed Neural Networks.SIAM Journal on Scientific Computing, 43(5):A3055–A3081, 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:54.882598Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:f8f70f8d16e3215efd8e3b236f6243eb461a567590fddc49d9a710ed7f70d222","observation_id":"d6adc7ef-bc6c-48ac-8230-f2a38637c501","resolution":{"observed_at":"2026-08-12T00:15:54.882598Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:54.897182Z","title":"Inverse Dirichlet weighting enables reliable training of physics informed neural networks.Machine Learning: Science and Technology, 3(1):015026, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:54.897182Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:63ae68216838d00f8a880f4a2fe7f1f237f01b65fac92d357ce71be4599862c0","observation_id":"1fe8694e-7850-4a05-a3d4-bd58d00f80ae","resolution":{"observed_at":"2026-08-12T00:15:54.897182Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:54.928815Z","title":"McClenny and Ulisses M","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:54.928815Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:090933af9a52d85e3fd7a72be8617ec49c74772781b56a8facc0f505e7cbd831","observation_id":"b285613f-13ac-43c8-8527-876ffd369ebf","resolution":{"observed_at":"2026-08-12T00:15:54.928815Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:54.939530Z","title":"Self-adaptive loss balanced Physics- informed neural networks.Neurocomputing, 496:11–34, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:54.939530Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:373130ae444306966796f7e1c9be739f75b711107cb1b9ecd32efae94ca7e8d1","observation_id":"7625d21a-0be9-422d-b442-ce1743e07536","resolution":{"observed_at":"2026-08-12T00:15:54.939530Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:54.974746Z","title":"Efficient Implementation of Weighted ENO Schemes.Journal of Computational Physics, 126(1):202–228, 1996","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:54.974746Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:e83e83963c0171846f7d9090d92ea83b48ba91ee596c62f0ca99ea77e0edcf39","observation_id":"d727b49b-22f8-4c39-abfe-5090ebf8bc2c","resolution":{"observed_at":"2026-08-12T00:15:54.974746Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:54.983554Z","title":"Efficient implementation of essentially non- oscillatory shock-capturing schemes.Journal of Computational Physics, 77(2):439– 471, 1988","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:54.983554Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:d1d200b23144662af4fc9d7450899e82900e3aa251ff6e13c1d8b1d0b4b6722f","observation_id":"fa932c0d-902f-4ae5-913c-0bf760d551ad","resolution":{"observed_at":"2026-08-12T00:15:54.983554Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:56.715670Z","title":"Srinivasan, Ben Mildenhall, Sara Fridovich-Keil, Nithin Raghavan, Utkarsh Singhal, Ravi Ramamoorthi, Jonathan T","venue":null,"work_id":"fc0782f4-e0bb-49c6-90ed-a7990b6b82f0","year":2020},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:54.994792Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:856b1dcd51195b853f298ce09a1bbdcf9cbc68d50f2403f6aa3a3f617523adb5","observation_id":"c476eaac-63cf-4565-b67d-8fd5d45d217e","resolution":{"observed_at":"2026-08-12T00:15:56.739361Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:55.013892Z","title":"Respecting causality for training physics-informed neural networks.Computer Methods in Applied Mechanics and Engineering, 421:116813, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:55.013892Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:eecc728bbea6e751c0a31f84ee2b2d2f16538c2bf809a50be32271eb536c215a","observation_id":"f00e3ab7-6717-41da-bbe1-5e48a6b1a591","resolution":{"observed_at":"2026-08-12T00:15:55.013892Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2002.7166","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:55.675913Z","title":"A Hybrid Parti- cle Level Set Method for Improved Interface Capturing.Journal of Computational Physics, 183(1):83–116, 2002","venue":null,"work_id":"3c13c8de-01e8-4fa4-a190-91519fa9d7a8","year":2002},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:55.039877Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:437d1f68e00998f844363519df74ef6cccca3fff04002c608d48f134a5727e9f","observation_id":"2e727807-fc48-4189-8f93-c1953c100491","resolution":{"observed_at":"2026-08-12T00:15:55.701642Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:56.666153Z","title":"Springer New York, 2003","venue":null,"work_id":"f391099e-64f9-4bd5-b88a-8517644284a0","year":2003},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:55.064257Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:4e54a74bffb27796246b6dff6e3c8921253073913efa45ae91de800bb76da2eb","observation_id":"1c7bc33c-d380-4edb-83de-1982375217e4","resolution":{"observed_at":"2026-08-12T00:15:56.670870Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:56.544743Z","title":"When and why PINNs fail to train: A neural tangent kernel perspective.Journal of Computational Physics, 449:110768,","venue":null,"work_id":"d4d0beed-f970-49e9-9fbc-31b6f9befd0d","year":null},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:55.069405Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:0d371e9bb0a66cff4eb700159562b519b22b41fbf5d97f223587e067dbe6b40a","observation_id":"a02ead75-3762-4c5b-8fc5-5831bdf04926","resolution":{"observed_at":"2026-08-12T00:15:56.604172Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.5281/zenodo.21852144","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:55.137352Z","title":"Eikonal regularization in physics-informed neural networks for three-dimensional level-set advection: Transferability of two-dimensional design principles — Source Code, 2026","venue":null,"work_id":"244816e1-8923-4108-bed2-cd9747de4d5c","year":2026},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:55.087825Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:8b89df953efe27f2e7a4536022d952232497d42075f8a45a3fb68c611ab2081a","observation_id":"60535a67-0f94-46fd-a042-5ee94aed401e","resolution":{"observed_at":"2026-08-12T00:15:55.164752Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-12T23:38:13.557377+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-12T23:38:13.557377+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:54.861047Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":2021,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:54.861047Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:cd272ae50301431283e3e9c6ef148b3428a99228f72607f0922dc40f58441855","observation_id":"4112c9f1-cdfc-4fc8-a291-30d45de0a733","resolution":{"observed_at":"2026-08-12T00:15:54.861047Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:15:55.074747Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles","version":1},"reference_index":2022,"source":"pdf_text","source_observed_at":"2026-08-12T00:15:55.074747Z"},"links":{"citing_paper":"/paper/2608.08322"},"observation_digest":"sha256:5c6a291d5527922e46ba621424f01c079496f96388cd371461225562ff68a7b7","observation_id":"a7ff5bb1-a3e8-4959-8318-46aebd16794e","resolution":{"observed_at":"2026-08-12T00:15:55.074747Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2608.08322","last_updated":"2026-08-08T20:20:13Z","latest_version":1,"primary_category":"physics.flu-dyn","snapshot_observed_at":"2026-08-13T23:30:18.714829Z","submitted_at":"2026-08-08T20:20:13Z","title":"Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles"},"reference_resolution":{"displayed":26,"state_counts":{"malformed_identifier":4,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":11,"verified_exact":3,"verified_fuzzy":8},"total_outbound_references":26},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2608.08322."}